Sin causes death. God causes Life. The opposite of sin is life. The opposite of life is death. Sin is therefore death and God is life. This means that anything that causes life is of God. All that is good edifies and all that destroys is bad and consequently a sin. Think of sin as everything and anything, ideas, substance, actions that rob the human being of the Life that belongs to God that he has placed in us.
We all die because at some point our own genome betrays us. Cells don't stop growing. They are constantly replenished until a signal is given for them to stop doing so. This is the beginning of the process of death. God gives us life not death. This rogue signal is not of God it is inherited from some point in our very distant past. Since all people as far as we know die then it must be traced back to our first parents or more exactly to something that they did to introduce this rogue gene (signal), perhaps eating something that was not meant for human ingestion.
We still do that today. Alcoholism can become an inherited trait, so can obesity, heart disease, etc. all things that stem from some form of modified behavior. So in short, yes we can inherit sin or more accurately the cause of sin in other words we can inherit the cause of death and as everyone can see by the evidence around us, we have.